Sphere packing and quantum gravity

doi:10.1007/JHEP12(2019)048

Sphere packing and quantum gravity

2019-12-05

70

OA

AI

DOI：10.1007/JHEP12(2019)048

原文链接

查看原文

摘要

En 中文

We establish a precise relation between the modular bootstrap, used to con- strain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra U(1)(c) maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in d = 2c dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For c = 4 and c = 12, these functionals exactly repro- duce the magic functions used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension Delta 0 less than or similar to c/8.503.

Keyword:

AdS-CFT Correspondence

Conformal Field Theory

Black Holes

Conformal and W Symmetry

Sphere packing and quantum gravity

摘要

AI总结

期刊

机构